GATE 2022 ES – Question 36
For $y^{\prime\prime}+4y=0$, y(0)=0 and $y^{\prime}(0)=1$, identify problem and solution.
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Correct answer: (C) Initial-value problem,$y=\frac12\sin2x$
Explanation
The two conditions are imposed at the same x=0, making an initial-value problem. General solution is $A\cos2x+B\sin2x$. The value condition gives A=0; derivative condition gives 2B=1. Hence **C**, $y=\frac12\sin2x$.